.TH std::ranges::is_heap 3 "2024.06.10" "http://cppreference.com" "C++ Standard Libary"
.SH NAME
std::ranges::is_heap \- std::ranges::is_heap

.SH Synopsis
   Defined in header <algorithm>
   Call signature
   template< std::random_access_iterator I, std::sentinel_for<I> S,

             class Proj = std::identity, std::indirect_strict_weak_order<       (since
             std::projected<I, Proj>> Comp = ranges::less >                 \fB(1)\fP C++20)
   constexpr bool

       is_heap( I first, S last, Comp comp = {}, Proj proj = {} );
   template< ranges::random_access_range R, class Proj = std::identity,


   std::indirect_strict_weak_order<std::projected<ranges::iterator_t<R>,        (since
   Proj>>                                                                   \fB(2)\fP C++20)
             Comp = ranges::less >
   constexpr bool

       is_heap( R&& r, Comp comp = {}, Proj proj = {} );

   Checks if the elements in range [first, last) are a max heap.

   1) Elements are compared using the given binary comparison function comp and
   projection object proj.
   2) Same as \fB(1)\fP, but uses r as the range, as if using ranges::begin(r) as first and
   ranges::end(r) as last.

   The function-like entities described on this page are niebloids, that is:

     * Explicit template argument lists cannot be specified when calling any of them.
     * None of them are visible to argument-dependent lookup.
     * When any of them are found by normal unqualified lookup as the name to the left
       of the function-call operator, argument-dependent lookup is inhibited.

   In practice, they may be implemented as function objects, or with special compiler
   extensions.

.SH Parameters

   first, last - the range of elements to examine
   r           - the range of elements to examine
   pred        - predicate to apply to the projected elements
   proj        - projection to apply to the elements

.SH Return value

   true if the range is max heap, false otherwise.

.SH Complexity

   Linear in the distance between first and last.

.SH Notes

   A max heap is a range of elements [f, l), arranged with respect to comparator comp
   and projection proj, that has the following properties:

     * With N = l - f, p = f[(i - 1) / 2], and q = f[i], for all 0 < i < N, the
       expression std::invoke(comp, std::invoke(proj, p), std::invoke(proj, q))
       evaluates to false.
     * A new element can be added using ranges::push_heap, in \\(\\scriptsize
       \\mathcal{O}(\\log N)\\)𝓞(log N) time.
     * The first element can be removed using ranges::pop_heap, in \\(\\scriptsize
       \\mathcal{O}(\\log N)\\)𝓞(log N) time.

.SH Possible implementation

 struct is_heap_fn
 {
     template<std::random_access_iterator I, std::sentinel_for<I> S,
              class Proj = std::identity, std::indirect_strict_weak_order<
              std::projected<I, Proj>> Comp = ranges::less>
     constexpr bool operator()(I first, S last, Comp comp = {}, Proj proj = {}) const
     {
         return (last == ranges::is_heap_until(first, last,
                                               std::move(comp), std::move(proj)));
     }

     template<ranges::random_access_range R, class Proj = std::identity,
              std::indirect_strict_weak_order<std::projected<ranges::iterator_t<R>, Proj>>
              Comp = ranges::less>
     constexpr bool operator()(R&& r, Comp comp = {}, Proj proj = {}) const
     {
         return (*this)(ranges::begin(r), ranges::end(r),
                        std::move(comp), std::move(proj));
     }
 };

 inline constexpr is_heap_fn is_heap {};

.SH Example


// Run this code

 #include <algorithm>
 #include <bit>
 #include <cmath>
 #include <iostream>
 #include <vector>

 void out(const auto& what, int n = 1)
 {
     while (n-- > 0)
         std::cout << what;
 }

 void draw_heap(auto const& v)
 {
     auto bails = [](int n, int w)
     {
         auto b = [](int w) { out("┌"), out("─", w), out("┴"), out("─", w), out("┐"); };
         n /= 2;
         if (!n)
             return;
         for (out(' ', w); n-- > 0;)
             b(w), out(' ', w + w + 1);
         out('\\n');
     };
     auto data = [](int n, int w, auto& first, auto last)
     {
         for (out(' ', w); n-- > 0 && first != last; ++first)
             out(*first), out(' ', w + w + 1);
         out('\\n');
     };
     auto tier = [&](int t, int m, auto& first, auto last)
     {
         const int n{1 << t};
         const int w{(1 << (m - t - 1)) - 1};
         bails(n, w), data(n, w, first, last);
     };
     const int m{static_cast<int>(std::ceil(std::log2(1 + v.size())))};
     auto first{v.cbegin()};
     for (int i{}; i != m; ++i)
         tier(i, m, first, v.cend());
 }

 int main()
 {
     std::vector<int> v{3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 5, 8, 9, 7, 9, 3, 2, 3, 8};

     out("initially, v:\\n");
     for (auto i : v)
         std::cout << i << ' ';
     out('\\n');

     if (!std::ranges::is_heap(v))
     {
         out("making heap...\\n");
         std::ranges::make_heap(v);
     }

     out("after make_heap, v:\\n");
     for (auto t{1U}; auto i : v)
         std::cout << i << (std::has_single_bit(++t) ? " │ " : " ");

     out("\\n" "corresponding binary tree is:\\n");
     draw_heap(v);
 }

.SH Output:

 initially, v:
 3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8
 making heap...
 after make_heap, v:
 9 │ 8 9 │ 6 5 8 9 │ 3 5 3 5 3 4 7 2 │ 1 2 3 1
 corresponding binary tree is:
                9
        ┌───────┴───────┐
        8               9
    ┌───┴───┐       ┌───┴───┐
    6       5       8       9
  ┌─┴─┐   ┌─┴─┐   ┌─┴─┐   ┌─┴─┐
  3   5   3   5   3   4   7   2
 ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐ ┌┴┐
 1 2 3 1

.SH See also

   ranges::is_heap_until finds the largest subrange that is a max heap
   (C++20)               (niebloid)
   ranges::make_heap     creates a max heap out of a range of elements
   (C++20)               (niebloid)
   ranges::push_heap     adds an element to a max heap
   (C++20)               (niebloid)
   ranges::pop_heap      removes the largest element from a max heap
   (C++20)               (niebloid)
   ranges::sort_heap     turns a max heap into a range of elements sorted in ascending
   (C++20)               order
                         (niebloid)
   is_heap               checks if the given range is a max heap
   \fI(C++11)\fP               \fI(function template)\fP
